In his first extended critique of the Republican National Convention, President Obama on Saturday mocked his rivals’ nominating stage show as outdated and uninspired, suggesting that the GOP was offering “an agenda better suited for the last century.”

Obama kicked off a four-day tour of swing states leading up to his arrival Wednesday at the Democratic National Convention, where on Thursday he will accept the nomination for a second term. Addressing about 10,000 supporters outside a farm museum in this rural town near Des Moines, Obama offered an assessment of Republican rival Mitt Romney, who formally accepted his party’s nomination last Thursday.

“It was something to behold,” Obama said sarcastically about the Republican convention in Tampa. “Despite all the chal­lenges we face . . . what they offered over those three days was more often than not an agenda better suited for the last century. It was a rerun. We’d seen it before. We might as well have watched it on a black-and-white TV.”

Obama was making his seventh appearance in Iowa this year. He credits the state with launching his 2008 victory, but statewide polls show a tight race between him and Romney. The president’s campaign said it is focused on states such as Iowa that allow non-absentee early voting, and Obama told Iowans to cast their ballots as soon as they are able to Sept. 27.

The Obama campaign has criticized Romney and his running mate, Rep. Paul Ryan (R-Wis.), for leveling personal attacks against the president but failing to provide specifics on their policy agenda last week. In his speech, Obama continued to draw a sharp contrast with Romney on energy, taxes and the end of the Iraq war, tying the GOP nominee’s policies to those of the George W. Bush administration.

“We heard a lot of talk about bold choices, but no one bothered to tell you what they were,” Obama said. “Gov. Romney did not offer a single new idea. . . . And they spent even less time talking about what they plan to do. Not just because they know you won’t like it, but because you lived through it and can’t afford to repeat it.”

Meanwhile, Romney, campaigning in Ohio and Florida on the opening weekend of the college football season, employed a game-day metaphor when he declared that it’s time for America to “get a new coach.”

Noting that Obama had promised during his 2008 campaign to create more jobs, Romney said that an unacceptably high number of people are out of work or have stopped looking for work or are underemployed.

“If you have a coach that’s zero and 23 million, you say it’s time to get a new coach. It’s time for America to see a winning season again, and we’re going to bring it to ’em,” Romney said to roaring applause from a couple of thousand supporters packed into an historic art deco train station in Cincinnati.

Ryan on Saturday campaigned in Columbus, Ohio — where his alma mater, Miami University, was playing Ohio State University in football — before reuniting with Romney for an afternoon rally in Jacksonville, Fla.

Trying to seize momentum coming out of the Republican convention, Romney recycled many of the lines from his acceptance speech there. He declared that many Americans are disappointed that Obama has not lived up to the promises of his historic campaign four years ago — a pitch to independent voters who backed the president in 2008 but are wavering this time around.

In his speech to an overflow crowd inside the grand Union Terminal, Romney sought to rise above the divisive tone set by both the Obama campaign and his own campaign this summer as he called on Americans to unite and pledged that he would be the one to bring a splintered nation together.

“We do not have to have the kind of divisiveness and bitterness and recriminations we’ve seen over the last four years,” Romney said. “I will bring us together . . . America’s going to come roaring back. A better future is ahead. It’s out there waiting for us. Our families deserve it. Our children demand it. The peace of the planet depends upon it. I love America. We’re taking this country back.”

Before Obama spoke in Iowa, his campaign spokeswoman, Jen Psaki, dismissed the Romney camp’s suggestion that they will get a significant bump in the polls from the Republican convention.

“It’s been a pretty steady race to date, and we expect it will be in a pretty similar place following our convention. We know it will be close,” Psaki said.

Rucker reported from Cincinnati and Jacksonville.